CalcRover

Ratio Calculator

Two ratio tools: simplify any ratio to lowest terms (decimals get cleared first), and solve a proportion A : B = C : x for the missing value. Steps show the GCF division and the cross-multiplication.

Simplify a ratio

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Solve a proportion: A : B = C : x

:=:?

Ratios and proportions

A ratio compares two quantities; it simplifies exactly like a fraction — divide both sides by their greatest common factor. Decimal terms are cleared first by multiplying both sides by a power of 10. The "1 : x" form is handy for comparing ratios with different terms.

A proportion states two ratios are equal. The cross-products rule says A × x = B × C, so the missing term is one multiplication and one division — the workhorse of scale models, recipes and map distances.

simplify: divide both terms by GCF
A : B = C : x → x = B × C ÷ A

Worked examples

Example 1: simplify 16 : 18

An aspect-ratio-style pair: reduce 16 : 18.

  1. GCF of 16 and 18 is 2.
    16 ÷ 2 : 18 ÷ 2
  2. Write the reduced ratio.
    8 : 9

16 : 18 = 8 : 9 (as a decimal, 0.889 : 1… inverted — 1 : 1.125).

Example 2: scale up a recipe

A dressing uses oil and vinegar 3 : 1. How much vinegar for 9 tbsp of oil?

  1. Set the proportion.
    3 : 1 = 9 : x
  2. Cross-multiply.
    3x = 1 × 9 → x = 3

3 tablespoons of vinegar.

Example 3: map scale

A map is 1 : 50,000. Two towns are 7.4 cm apart on paper — real distance?

  1. Proportion with the map scale.
    1 : 50,000 = 7.4 : x
  2. Cross-multiply and convert.
    x = 370,000 cm = 3.7 km

3.7 kilometers in the real world.

FAQ

Are ratios and fractions the same thing?+

Closely related: the ratio a : b corresponds to the fraction a/b, and both reduce by the GCF. The difference is reading — 3 : 1 compares parts to parts, while 3/4 usually means part of a whole.

How do I simplify a ratio with decimals?+

Multiply both sides by 10 until both are whole (2.5 : 1.5 → 25 : 15), then divide by the GCF → 5 : 3. The calculator does exactly that and shows it.

What's the 1 : x form for?+

Comparing ratios quickly — 8 : 9 vs 7 : 8 is hard to eyeball, but 1 : 1.125 vs 1 : 1.143 isn't. Screens, gears and dilution instructions all use it.

Can a ratio have three terms?+

Yes (concrete mix 1 : 2 : 3 is cement : sand : gravel) — simplify by the GCF of all three. Three-term input is planned; today you can simplify pairs at a time.

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